GA Sandbox

The GA Sandbox is two things: a starting point to use geometric algebra in your C++ programs, and a set of programming examples. The programming examples are discussed in detail in the book, at the end of each chapter (in Chapters 1 through 16).

The GA Sandbox contains the following geometric algebra implementations:

• e2ga: The vector space model of 2-D space.
• e3ga: The vector space model of 3-D space (mainly used in Chapters 2 through 10).
• h3ga: The homogeneous model of 3-D space (mainly used in Chapters 11 and 12).
• c2ga: The conformal model of 2-D space.
• c3ga: The conformal model of 3-D space (mainly used in Chapters 13 through 16).

These implementations were generated using Gaigen 2. The algebra specifications are included in the package, so you can use Gaigen 2 to re-generate the source files, if you would have the need to do so.

The GA Sandbox is hosted on SourceForge.net. To download it, you may go directly to the file download page. We also have a set of screenshots of the programming examples in action.

Online Viewing of Source Code

You may also browse the example source code online using the list below. Most links jump directly to the interesting part of the file. For some examples there are multiple source files of interest. At the bottom of the page, you can also find links to two geometric algebra implementations (e2ga and c2ga), and the Gaigen 2 specifications and profiles from which these implementations were generated.

Section	Name	File	Model
1.1	An Example in Geometric Algebra	chap1ex1.cpp	3-D Conformal
.
	Basic Theory
2.13.1	Drawing Bivectors	chap2ex1.cpp	2-D Vector Space
2.13.2	Hidden Surface Removal	chap2ex2.cpp	3-D Vector Space
2.13.3	Singularities in Vector Fields	hpindex.cpp	3-D Vector Space
		fields.cpp
3.11.1	Orthonormalization	chap3ex1.cpp	3-D Vector Space
3.11.2	Implementing the Cross Product	chap3ex2.cpp	3-D Vector Space
3.11.3	Reciprocal Frames	chap3ex3.cpp	3-D Vector Space
		e3ga_util.cpp
3.11.4	Color Space Conversion	chap3ex4.cpp	3-D Vector Space
.
4.9.1	Orthogonal Projection	chap4ex1.cpp	3-D Vector Space
4.9.2	Orth. Proj, Matrix Representation	chap4ex2.cpp	3-D Vector Space
4.9.3	Transforming Normal Vectors	chap4ex3.cpp	3-D Vector Space
.
5.11.1	The Meet and Join	chap5ex1.cpp	3-D Vector Space
5.11.2	Efficiency	chap5ex2.cpp	3-D Vector Space
5.11.3	Floating Point Issues	chap5ex3.cpp	3-D Vector Space
.
6.7.1	Subspace Products Retrieved	chap6ex1.cpp	3-D Vector Space
6.7.2	Gram-Schmidt Orthogonalization	chap6ex2.cpp	3-D Vector Space
.
7.10.1	Reflecting in Vectors	chap7ex1.cpp	3-D Vector Space
7.10.2	Two Reflections Equal One Rotation	chap7ex2.cpp	3-D Vector Space
7.10.3	Matrix-Rotor Conversion 1	chap7ex3.cpp	3-D Vector Space
7.10.4	Matrix-Rotor Conversion 2	chap7ex4.cpp	3-D Vector Space
7.10.5	Julia Fractals	chap7ex5.cpp	2-D Vector Space
.
	Vector Space Model
10.7.1	Interpolating Rotations	chap10ex1.cpp	3-D Vector Space
10.7.2	Crystallography	chap10ex2.cpp	3-D Vector Space
10.7.3	External Camera Calibration	chap10ex3.cpp	3-D Vector Space
		extcalibrefine.cpp
	Homogeneous Model
11.13.1	Working with Points	chap11ex1.cpp	3-D Homogeneous
11.13.2	Intersecting Primitives	chap11ex2.cpp	3-D Homogeneous
11.13.3	Don't Add Lines	chap11ex3.cpp	3-D Homogeneous
11.13.4	Perspective Projection	chap11ex4.cpp	3-D Homogeneous
.
12.5.1	Loading Transformations	chap12ex1.cpp	3-D Homogeneous
	into OpenGL
12.5.2	Transforming Primitives	chap12ex2.cpp	3-D Homogeneous
	with OpenGL Matrices
12.5.3	Marker Reconstruction	chap12ex3.cpp	3-D Homogeneous
	in Optical Motion Capture	reconstruct.cpp
.
	Conformal Model
13.10.1	Metric Matters	chap13ex1.cpp	3-D Conformal
13.10.2	The Distance Between Points	chap13ex2.cpp	3-D Conformal
13.10.3	Loading Transformations	chap13ex3.cpp	3-D Conformal
	into OpenGL, Again
13.10.4	Interpolation of	chap13ex4.cpp	3-D Conformal
	Rigid Body Motions
.
14.9.1	Voronoi Diagrams and	chap14ex1.cpp	3-D Conformal
	Delaunay Triangulations
14.9.2	Drawing Euclid's Elements	chap14ex2.cpp	3-D Conformal
14.9.3	Conformal Primitives and	chap14ex3.cpp	3-D Conformal
	Intersections
14.9.4	Fitting a Sphere to	chap14ex4.cpp	3-D Conformal
	a Set of Points
.
15.8.1	The Plunge	chap15ex1.cpp	3-D Conformal
15.8.2	Affine Combinations of Points	chap15ex2.cpp	3-D Conformal
15.8.3	Euclidean Projections	chap15ex3.cpp	3-D Conformal
.
16.10.1	Homogeneous 4x4 Matrices to	chap16ex1.cpp	3-D Conformal
	Conformal Versors	c3ga_util.cpp
16.10.2	Logarithm of	chap16ex2.cpp	3-D Conformal
	Scaled Rigid Body Motion	c3ga_util.cpp
16.10.3	Interpolation of	chap16ex3.cpp	3-D Conformal
	Scaled Rigid Body Motions
16.10.4	The Sea Shell	chap16ex4.cpp	3-D Conformal
.
	Miscellaneous
---------------	E2GA implementation	e2ga.cpp	2-D Vector Space
---------------	E2GA implementation	e2ga.h	2-D Vector Space
---------------	C2GA implementation	c2ga.cpp	2-D Conformal
---------------	C2GA implementation	c2ga.h	2-D Conformal
---------------	E3GA utilities	e3ga_util.cpp	3-D Vector Space
---------------	H3GA utilities	h3ga_util.cpp	3-D Homogeneous
---------------	C3GA utilities	c3ga_util.cpp	3-D Conformal
.
	Specifications
---------------	E2GA specification	e2ga.gs2	2-D Vector Space
---------------	E2GA profile	e2ga.gp2	2-D Vector Space
---------------	E3GA specification	e3ga.gs2	3-D Vector Space
---------------	E3GA profile	e3ga.gp2	3-D Vector Space
---------------	H3GA specification	h3ga.gs2	3-D Homogeneous
---------------	H3GA profile	h3ga.gp2	3-D Homogeneous
---------------	C2GA specification	c2ga.gs2	2-D Conformal
---------------	C2GA profile	c2ga.gp2	2-D Conformal
---------------	C3GA specification	c3ga.gs2	3-D Conformal
---------------	C3GA profile	c3ga.gp2	3-D Conformal

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